Fast diffusion and electromigration of metallic solutes in thorium

A classification of the behaviour of the solutions f(·, a) to the ordinary differential equation (|f′|p-2f′)′ + f - |f′|p-1 = 0 in (0,∞) with initial condition f(0, a) = a and f′(0, a) = 0 is provided, according to the value of the parameter a > 0 when the exponent p takes values in (1, 2). There is a threshold value a* that separates different behaviours of f(·, a): if a > a*, then f(·, a) vanishes at least once in (0,∞) and takes negative values, while f(·, a) is positive in (0,∞) and decays algebraically to zero as r→∞ if a ∊ (0, a*). At the threshold value, f(·, a*) is also positive in (0,∞) but decays exponentially fast to zero as r→∞. The proof of these results relies on a transformation to a first-order ordinary differential equation and a monotonicity property with respect to a > 0. This classification is one step in the description of the dynamics near the extinction time of a diffusive Hamilton–Jacobi equation with critical gradient absorption and fast diffusion.

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Fast Diffusion of the Unassembled PetC1-GFP Protein in the Cyanobacterial Thylakoid Membrane

Life ◽

10.3390/life11010015 ◽

2020 ◽

Vol 11 (1) ◽

pp. 15

Author(s):

Radek Kaňa ◽

Gábor Steinbach ◽

Roman Sobotka ◽

György Vámosi ◽

Josef Komenda

Keyword(s):

Membrane Proteins ◽

Single Molecule ◽

Protein Interactions ◽

Thylakoid Membrane ◽

Protein Complexes ◽

Correlation Spectroscopy ◽

Membrane Microdomains ◽

Fast Diffusion ◽

Light Harvesting Complexes ◽

Term Survival

Biological membranes were originally described as a fluid mosaic with uniform distribution of proteins and lipids. Later, heterogeneous membrane areas were found in many membrane systems including cyanobacterial thylakoids. In fact, cyanobacterial pigment–protein complexes (photosystems, phycobilisomes) form a heterogeneous mosaic of thylakoid membrane microdomains (MDs) restricting protein mobility. The trafficking of membrane proteins is one of the key factors for long-term survival under stress conditions, for instance during exposure to photoinhibitory light conditions. However, the mobility of unbound ‘free’ proteins in thylakoid membrane is poorly characterized. In this work, we assessed the maximal diffusional ability of a small, unbound thylakoid membrane protein by semi-single molecule FCS (fluorescence correlation spectroscopy) method in the cyanobacterium Synechocystis sp. PCC6803. We utilized a GFP-tagged variant of the cytochrome b6f subunit PetC1 (PetC1-GFP), which was not assembled in the b6f complex due to the presence of the tag. Subsequent FCS measurements have identified a very fast diffusion of the PetC1-GFP protein in the thylakoid membrane (D = 0.14 − 2.95 µm2s−1). This means that the mobility of PetC1-GFP was comparable with that of free lipids and was 50–500 times higher in comparison to the mobility of proteins (e.g., IsiA, LHCII—light-harvesting complexes of PSII) naturally associated with larger thylakoid membrane complexes like photosystems. Our results thus demonstrate the ability of free thylakoid-membrane proteins to move very fast, revealing the crucial role of protein–protein interactions in the mobility restrictions for large thylakoid protein complexes.

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Effect of Macropore Structure on Desorption Diffusion Performance of N-Pentane on 5A Zeolite

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.634-638.731 ◽

2013 ◽

Vol 634-638 ◽

pp. 731-735 ◽

Cited By ~ 1

Author(s):

Lu Shi ◽

Zong Jian Liu ◽

Qun Cui ◽

Hai Yan Wang ◽

Hu Qing Yao

Keyword(s):

Diffusion Coefficients ◽

Diffusion Rate ◽

Low Pressure ◽

Fast Diffusion ◽

Desorption Rate ◽

Macropore Structure ◽

5A Zeolite ◽

Desorption Equilibrium

Desorption rate curves of n-pentane on 5A zeolites at 418 K and 10-0.03 kPa were determined, and the effects of different macropore structure on desorption performance were analyzed. Results show that macropore distribution of 5A-1 concentrates in 0.25-1.25 μm, while that of 5A-2 ranges from mesopore category to 0.3 μm, but 5A-3 contains both pores of 0.01-0.1 μm and 0.2-2 μm inside, reflecting a broadest distribution; 5A-3, 5A-1 and 5A-2 reach desorption equilibrium after 1100 s, 1400 s and 2000 s respectively at 0.03 kPa, indicating that abundant macropores make n-pentane fastest desorbed from 5A-3, but this advantage gradually disappears with the increasing pressure; the effective desorption diffusion coefficients of n-pentane on 5A-1, 5A-2 and 5A-3 are 4.2×10-15-2.2×10-14 m2/s, 2.0×10-15-2.3×10-14 m2/s, 7.4×10-15-2.4×10-14 m2/s respectively, suggesting that plenty macropores make the diffusivity less affected by the changes of pressure, which can guarantee a fast diffusion rate of n-pentane even at low pressure.

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Poincaré inequalities for linearizations of very fast diffusion equations

Nonlinearity ◽

10.1088/0951-7715/15/3/303 ◽

2002 ◽

Vol 15 (3) ◽

pp. 565-580 ◽

Cited By ~ 17

Author(s):

J A Carrillo ◽

C Lederman ◽

P A Markowich ◽

G Toscani

Keyword(s):

Diffusion Equations ◽

Fast Diffusion ◽

Poincaré Inequalities ◽

Poincare Inequalities ◽

Fast Diffusion Equations

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On the equation ut = ∆uα + uβ

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500025750 ◽

1993 ◽

Vol 123 (2) ◽

pp. 373-390 ◽

Cited By ~ 24

Author(s):

Yuan-Wei Qi

Keyword(s):

Dynamical System ◽

Blow Up ◽

Uniqueness Result ◽

Fast Diffusion ◽

Negative Solution ◽

Fast Diffusion Equation ◽

Infinite Dimensional ◽

The Cauchy Problem ◽

Dimensional Dynamical System ◽

Infinite Dimensional Dynamical System

SynopsisThe Cauchy problem of ut, = ∆uα + uβ, where 0 < α < l and α>1, is studied. It is proved that if 1< β<α + 2/n then every nontrivial non-negative solution is not global in time. But if β>α+ 2/n there exist both blow-up solutions and global positive solutions which decay to zero as t–1/(β–1) when t →∞. Thus the famous Fujita result on ut = ∆u + up is generalised to the present fast diffusion equation. Furthermore, regarding the equation as an infinite dimensional dynamical system on Sobolev space W1,s (W2.s) with S > 1, a non-uniqueness result is established which shows that there exists a positive solution u(x, t) with u(., t) → 0 in W1.s (W2.s) as t → 0.

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